The essential adjointness of pseudo-differential operators on $\mathbb{Z}^n$
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866912005568331776 |
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| author | Milatovic, Ognjen |
| author_facet | Milatovic, Ognjen |
| contents | In the setting of the lattice $\mathbb{Z}^n$ we consider a pseudo-differential operator $A$ whose symbol belongs to a class defined on $\mathbb{Z}^n\times \mathbb{T}^n$, where $\mathbb{T}^n$ is the $n$-torus. We realize $A$ as an operator acting between the discrete Sobolev spaces $H^{s_j}(\mathbb{Z}^n)$, $s_j\in\mathbb{R}$, $j=1,2$, with the discrete Schwartz space serving as the domain of $A$. We provide a sufficient condition for the essential adjointness of the pair $(A,\,A^{\dagger})$, where $A^{\dagger}$ is the formal adjoint of $A$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_11216 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The essential adjointness of pseudo-differential operators on $\mathbb{Z}^n$ Milatovic, Ognjen Functional Analysis In the setting of the lattice $\mathbb{Z}^n$ we consider a pseudo-differential operator $A$ whose symbol belongs to a class defined on $\mathbb{Z}^n\times \mathbb{T}^n$, where $\mathbb{T}^n$ is the $n$-torus. We realize $A$ as an operator acting between the discrete Sobolev spaces $H^{s_j}(\mathbb{Z}^n)$, $s_j\in\mathbb{R}$, $j=1,2$, with the discrete Schwartz space serving as the domain of $A$. We provide a sufficient condition for the essential adjointness of the pair $(A,\,A^{\dagger})$, where $A^{\dagger}$ is the formal adjoint of $A$. |
| title | The essential adjointness of pseudo-differential operators on $\mathbb{Z}^n$ |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2208.11216 |